At the initial deployment of B-ISDN, the heterogeneity of services and the bandwidth requirement make dimensioning of B-ISDN much more complicated than the dimensioning of homogeneous circuit or packet switched networks. Therefore B-ISDN must be extended gradually according to future telecommunication technology or service demands. In this paper, we propose a mathematical formulation for dimensioning problem of B-ISDN extension, considering the characteristics of ATM(Asynchronous Transfer Mode) such as various quality of services, the statistical multiplexing effects of VPCs(Virtual Path Connections) and the modularity of transmission links allocated when new B-ISDN nodes are given. The algorithm based on the simultaneous linear approximation technique and Lagrangian relaxation method and some numerical results are also presented.